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Given: ∠A and ∠B are complementary angles. m∠A=3x+105 ; m∠B=−6x−39 Prove: m∠B=9° Drag and drop reasons into the boxes to correctly complete the proof. Statement Reason
∠A and ∠B are complementary angles. Given
m∠A=3x+105 ; m∠B=−6x−39 Given
m∠A+m∠B=90° Definition of complementary angles
3x+105−6x−39=90 Substitution Property of Equality
−3x+105−39=90 Simplify.
−3x+66=90 Simplify.
−3x=24
 x=−8
 m∠B=−6(−8)−39
 m∠B=48−39 Simplify.
m∠B=9°

Respuesta :

Given: [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

[tex]m \angle A = 3x+105^\circ[/tex] and [tex]m \angle B = -6x-39^\circ[/tex].

To prove: [tex]m \angle B = 9^\circ[/tex]

Proof:

Statement 1: [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

Reason 1: Given

Statement 2: [tex]m \angle A = 3x+105^\circ[/tex] and [tex]m \angle B = -6x-39^\circ[/tex].

Reason 2: Given

Statement 3: [tex]m \angle A + m \angle B = 90^\circ[/tex]

Reason 3: Definition of complementary angles.

Statement 4: [tex]3x+105^\circ -6x -39^\circ = 90^\circ[/tex]

Reason 4: Substitution property of equality

Statement 5: [tex]-3x+105^\circ-39^\circ = 90^\circ[/tex]

Reason 5: Simplification

Statement 6: [tex]-3x+66^\circ = 90^\circ[/tex]

Reason 6: Simplification

Statement 7: [tex]-3x = 24^\circ[/tex]

Reason 7:  Simplification

Statement 8: [tex]x = -8[/tex]

Reason 8: Multiplication property of equality

Statement 9: [tex]m \angle B = -6(-8) - 39^\circ[/tex]

Reason 9: Substituting the value of 'x'

Statement 10: [tex]m \angle B = 48-39 = 9^\circ[/tex]

Reason 10: Simplification


lublana

Answer:

Statement: -3x=90-66

Reason: By subtraction property of equality..

Statement: -3x=24

Reason: By simplification.

Statement: x=[tex]\frac{24}{-3}[/tex]

Reason: By division property of equality.

Statement: [tex]m\angle B= -6(-8)-39[/tex]

Reason: By substitution property of equality.

Statement: [tex]m\angle B=9^{\circ}[/tex]

Reason: By simplification.

Step-by-step explanation:

Given [tex]\angle A[/tex] and [tex]\angle B[/tex] are complementary angles.

[tex]m\angle A= 3x+105[/tex]

[tex]m\angle B=-6x-39[/tex]

To prove that [tex]m\angle B=9^{\circ}[/tex]

Proof:

1.Statement:[tex]\angle A\; and\; \angle B[/tex] are complementary angles .

Reason: Given .

2.Statement:  [tex]m\angle A=3x+105[/tex]; [tex]m\angle B= -6x-39[/tex]

Reason: Given .

3. Statement: [tex]m\angle A+ m\angle B=90^{\circ}[/tex]

Reason: By definition of complementary angles.

4.Statement:[tex]3x+105-6x-39=90[/tex]

Reason: By substitution  property of equality.

5. Statement: [tex]-3x+105-39=90[/tex]

Reason: By simplification.

6. Statement:  [tex]-3x+66=90[/tex]

Reason: By simplification.

7. Statement: [tex]-3x= 90-66[/tex]

Reason: By subtraction property of equality .

8.Statement:[tex]-3x=24[/tex]

Reason: By simplification.

9.Statement: [tex]x=\frac{24}{-3}[/tex]

Reason : By division property of equality.

10. Statement: x=-8

Reason: By simplification.

11. Statement: [tex]m\angle B= -6(-8)-39[/tex]

Reason : By substitution property of equality.

12. Statement: [tex]m\angle B= 48-39[/tex]

Reason: By simplification.

13. Statement: [tex]m\angle B=9^{\circ}[/tex]

Reason : By simplification.

Hence, [tex]m\angle B= 9^{\circ}[/tex]

Hence proved.

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